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I.
PREREQUISITES
Math 113, Algebra, or four years of high school mathematics.
II.
COURSE DESCRIPTION
| Section
1: |
Definition of a matrix. Algebraic operations on the set of matrices.
Solutions of systems of linear equations by the reduction of the augmented
matrix to row echelon form. Identity matrix and scalar matrix. Inverse
of a matrix and solving a linear system by using the inverse of the
matrix of coefficients (provided it exists.) |
| Section
2: |
Determinants. Row and column expansions. Adjoint of a matrix and finding
the inverse of a matrix by using the adjoint matrix. Cramer’s
Rule. |
| Section
3: |
Vector spaces and subspaces. Linear dependence and linear independence.
Basis and dimension of a vector space. Rank and nullity of a matrix
and the rank-nullity theorem. |
| Section
4: |
Linear transformations. Matrix of a linear transformation relative
to a specified basis. |
| Section
5: |
Inner products, orthonormal bases. Gram-Schimdt process for finding
an orthonormal basis. |
| Section
6: |
Characteristic polynomial, eigenvalues and eigenvectors of a square
matrix. Cayley-Hamilton theorem. Diagonalization. |
III.
TEXTBOOK AND SUPPLIES
Elementary Linear Algebra, by Munukutla S.K. Sastry, 1999. Supplied
with the course material and covered by the tuition.
| STUDENTS
ARE STRONGLY ADVISED NOT TO BUY TEXTBOOKS UNTIL REGISTERED
IN COURSES AS REQUIRED EDITIONS CAN CHANGE WITHOUT NOTICE. |
IV.
NATURE OF THE EXAMINATION
The examination consists of problems covering all sections of the textbook.
You will have some choice of problems. Three hours is allowed for the
examinations; you are not permitted to use books, notes, or supplementary
aids.
V.
GRADING CRITERIA
All problems are equally weighted for a total of 100 points for the examination.
Your grade will be based on the total points achieved on the examination
according to the following scale:
90 - 100 = A- to
A
80 - 89 = B- to B+
70 - 79 = C- to C+
69 - 60 = D- to D+
Below 60 = F
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